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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 3 — Jan. 31, 2011
  • pp: 2286–2293
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Slow non-dispersing wavepackets

Kyoung-Youm Kim, Chi-Young Hwang, and Byoungho Lee  »View Author Affiliations


Optics Express, Vol. 19, Issue 3, pp. 2286-2293 (2011)
http://dx.doi.org/10.1364/OE.19.002286


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Abstract

We show that in plasmonic or metamaterial slab waveguides, it is possible to generate slow non-dispersing wavepackets which undergo neither spatial diffraction nor temporal spreading with no nonlinear effects by forming a type of hybrid wavepacket between slow-light waveguide modes and diffraction-free Airy wavepackets. Three mechanisms are involved in their slowness: the slow-light feature of waveguide modes, the initial launching speed of hybrid wavepackets, and their acceleration along the time domain in a moving frame.

© 2011 Optical Society of America

Diffraction-free beams are a special class of light field configurations whose transverse intensity profiles are localized (i.e., they have a definite peak in amplitude) and remain invariant as they propagate through an optical medium. In recent years, these nondiffracting beams have been a subject of significant research interest and several types, such as Bessel [1

1. J. Durnin, J. J. Miceli Jr., and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987). [CrossRef] [PubMed]

], Mathieu [2

2. J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, and S. Chávez-Cerda, “Alternative formulation for invariant optical fields: Mathieu beams,” Opt. Lett. 25(20), 1493–1495 (2000). [CrossRef]

], and Airy beams [3

3. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901 (2007). [CrossRef]

, 4

4. G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32(8), 979–981 (2007). [CrossRef] [PubMed]

], have been analyzed theoretically and have actually been observed experimentally. From the practical point of view, Airy beams are very attractive, because they are accelerated (or self-bending) as they propagate and are the only nondiffracting example in the most simple (1+1)D configurations. These advantages have been exploited in several applications including optical trapping/particle manipulation [5

5. J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photon. 2(11), 675–678 (2008). [CrossRef]

, 6

6. H. Cheng, W. Zang, W. Zhou, and J. Tian, “Analysis of optical trapping and propulsion of Rayleigh particles using Airy beam,” Opt. Express 18(19), 20384–20394 (2010). [CrossRef] [PubMed]

], plasma waveguiding [7

7. P. Polynkin, M. Koleskik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324(5924), 229–232 (2009). [CrossRef] [PubMed]

], tomography [8

8. M. Asorey, P. Facchi, V. I. Man’ko, G. Marmo, S. Pascazio, and E. C. G. Sudarshan, “Generalized tomographic maps,” Phys. Rev. A 77(4), 042115 (2008). [CrossRef]

], and the implementation of Airy plasmons [9

9. A. Salandrino and D. N. Christodoulides, “Airy plasmon: a nondiffracting surface wave,” Opt. Lett. 35(12), 2082–2084 (2010). [CrossRef] [PubMed]

], optical bullets [10

10. A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photon. 4(2), 103–106 (2010). [CrossRef]

], and dual Airy beams [11

11. C.-Y. Hwang, D. Choi, K.-Y. Kim, and B. Lee, “Dual Airy beam,” Opt. Express 18(22), 23504–23516 (2010). [CrossRef] [PubMed]

]. Meanwhile, the wave equations for electric and magnetic fields of light include second-order derivative terms with respect to both space and time coordinates in a nearly identical way, which enables a temporal version of an Airy beam to be obtained, i.e., an Airy wavepacket [4

4. G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32(8), 979–981 (2007). [CrossRef] [PubMed]

, 10

10. A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photon. 4(2), 103–106 (2010). [CrossRef]

]. It retains the diffraction-free properties, which are now in the time domain (i.e., non-spreading property). Therefore, it can be regarded as a kind of soliton available without nonlinear effects. In this paper, we show that, in plasmonic or metamaterial waveguides which support slow-light modes, slow non-dispersing wavepackets which undergo neither spatial diffraction nor temporal spreading can be constructed via the association of these Airy wavepackets with slow-light waveguide modes and spatial Airy beams.

Schemes for slow light propagation based on plasmonic or metamaterial waveguides have been extensively studied in recent years [12

12. M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett. 93(13), 137404 (2004). [CrossRef] [PubMed]

]–[18

18. A. R. Davoyan, I. V. Shadrivov, A. A. Zharov, D. K. Gramotnev, and Y. S. Kivshar, “Nonlinear nanofocusing in tapered plasmonic waveguides,” Phys. Rev. Lett. 105(11), 116804 (2010). [CrossRef] [PubMed]

]. They took advantage of the competition between two opposite power flows in the core and clad layers and it is possible to implement slow light or light trapping when two opposite flows nearly compensate for one another. For example, in a waveguide made of a negative-index core and glass clads with propagation axis z, the optical power flows backward, i.e., along the −z direction in the core (since both the permittivity ɛ and permeability μ are negative) while it flows forward in the clads [19

19. K.-Y. Kim, I.-M. Lee, and B. Lee, “Grating-induced dual mode couplings in the negative-index slab waveguide,” IEEE Photon. Technol. Lett. 21(20), 1502–1504 (2009). [CrossRef]

]. These opposite power flows can form dual modes [one with a core-dominant/backward power flow and the other having a clad-dominant/forward power flow; see their exemplary mode profiles shown in Fig. 1(a)] which have small group velocities. In practice, they are advantageous, in that low temperatures are not required for operation. For example, let us consider a slab composed of a 0.539-μm negative-index layer between glass clads. We will consider only TM-polarized waveguide modes throughout this paper for the sake of simplicity, but TE cases can be dealt with quite similarly. For the modeling of dispersive properties, we adopted the Sellmeier equation for the glass and the Drude model for the negative-index layer: ɛco=1ωp,ɛ2/ω2 for permittivity and μco=1ωp,μ2/ω2 for permeability where ωp,ɛ and ωp,μ are so determined that we have ɛco = −4 and μco = −2 at λ0 = 1550 nm (f0 = 193.414 THz) [19

19. K.-Y. Kim, I.-M. Lee, and B. Lee, “Grating-induced dual mode couplings in the negative-index slab waveguide,” IEEE Photon. Technol. Lett. 21(20), 1502–1504 (2009). [CrossRef]

]. Figure 1(a) shows a plot of the effective indexes of the dual modes, where the upper and lower branches denote the backward and forward modes, respectively. We also show calculated group velocities and group velocity dispersions in Figs. 1(b) and 1(c), respectively.

Fig. 1 Effective indexes (neff) (a), group velocities (vg) (b), and group velocity dispersions (β2) (c) of TM-polarized dual modes in a negative-index-core waveguide. The solid blue and green dotted lines correspond to the backward and forward modes, respectively, and their exemplary transverse profiles are shown in (a). At f0 = 193.414 THz, we can obtain slow-light modes: a backward mode having neff = −1.8642, vg = c/92.8, β2 = 6.358 × 10−19, and a forward one with neff = 1.7908, vg = c/88.6, β2 = 6.339×10−19. They also have β3 = ∂β2/∂ω = 4.143 × 10−30 and 4.488 × 10−30, respectively.

Let us consider a TM-polarized electromagnetic pulse propagating in such a waveguide (see Fig. 2). We assume that its magnetic (Hx) field can be written as
ϕ=AT(t,z)AS(x,z)g(y)exp[j(β0zω0t)],
(1)
where ω0 is the carrier frequency of the pulse and β0 is the wavenumber at ω0. Assuming AT and AS are slowly varying functions of z and following a similar procedure as reported in [20

20. G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, San Diego, 2001).

], we can obtain separate equations for g, AS, and AT:
2gy2+[ω02c2ɛ(y)μ(y)β2]g=0,
(2)
jASz+12β02ASx2=0,
(3)
jATzβ222ATτ2+jB33ATτ3=0,
(4)
where ɛ(y) and μ(y) describe the relative permittivity and permeability of the layers in a slab, B = −(3β2/vg + β0β3)/(2β0) where vg = (∂β/∂ω|ω0)−1, β2 = 2β/∂ω2|ω0, and β3 = 3β/∂ω3|ω0, and a transformation of τ = t − (z/vg) where τ denotes time in a reference frame moving at the group velocity vg is introduced. From Eq. (2), we can see that g(y) denotes the transverse profile of a waveguide mode having propagation constant β at ω0. It should be noted that in deriving Eq. (4), we retained the dispersive property of β(ω) up to the third order.

Fig. 2 Concept of a slow non-dispersing wavepacket. g(y) denotes the transverse profile of dual slow-light modes at the carrier frequency ω0. (a) and (b) Initial fields for the launching of slow non-dispersing wavepackets associated with backward and forward slow-light modes, respectively.

The calculated profiles of the hybrid wavepackets at the center of the core of the waveguide in Fig. 1 are plotted in Fig. 3. We assumed the central frequency of the wavepackets to be f0 = 193.414 THz. We note they experience a slight diffraction and spreading along the spatial and temporal coordinates due to finite energy (i.e., non-zero aS and aT) carried by them [3

3. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901 (2007). [CrossRef]

, 4

4. G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32(8), 979–981 (2007). [CrossRef] [PubMed]

]. We assumed aS = 0.1 + 2j, aT = 0.05 − j, x0 = 1.5λ0, and τ0 = 6.5 ps. We launch at z = 0 the initial field Ai(x/x0) exp(aSx/x0Ai(t/τ0) exp(aTt/τ0). It experiences oscillatory-to-decaying conversions near t = 0 and x = 0, generating a peak as can be seen in Figs. 2(a) and 2(b). This peak is accelerated along two transverse directions: one along the +x and the other along +τ coordinates (see Fig. 4). The former acceleration is due to that of the spatial Airy beam AS(x, z) and indicates a spatial shift in the local intensity peak of the beam. The latter results from that of the Airy wavepacket AT (τ,z) and the acceleration along τ can be interpreted as a slowdown of the local intensity peak of the wavepacket. Here we claim that this acceleration can slow down the slow non-dispersing wavepacket further. However, it should be noted that the velocity, which slows down here, denotes a phenomenal speed, i.e., that of the local intensity peak of the hybrid wavepacket [23

23. The speed of the center-of-mass position of the hybrid wavepacket remains invariant. Refer to [3] and M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys. 47(3), 264–267 (1979) for more details. [CrossRef]

].

Fig. 3 Intensity profiles of slow non-dispersing wavepackets through the waveguide analyzed in Fig. 1. (a)–(c) Propagating profiles of a slow non-dispersing wavepacket associated with the backward mode. (d)–(f) The same as (a)–(c) associated with the forward one. The average speeds of non-dispersing wavepackets in their peak positions are reduced by as much as 0.0045c0 and 0.0040c0, respectively, although vg of the slow-light modes is about 0.011c0 where c0 is the speed of light in a vacuum. Two additional factors contribute to this slowdown: one being the initial launching speed of hybrid wavepackets and the other their acceleration along the time domain in a moving frame (see Fig. 5 for details).
Fig. 4 (a), (b) Propagating profiles (at z = 0, 10λ0, 20λ0, 30λ0, 40λ0, 50λ0) of temporal Airy wavepackets AT (τ,z) associated with backward and forward slow-light modes, respectively. Note that the transverse direction indicates time in a moving frame (τ) and the acceleration along τ can be interpreted as a slowdown of the local intensity peak of the wavepacket. (c), (d) The same as (a) and (b) for spatial Airy beams AS(x, z) (at z = 0, 10λ0, 30λ0, 50λ0)), in which the acceleration indicates a spatial shift in the local intensity peak of the beam. (e) Spatial trajectories of the slow non-dispersing wavepackets.

Let us check this in more detail. By putting the real parts of the Airy function arguments to zero (see Eq. (6)), we can obtain the temporal trajectory of the slow non-dispersing wavepacket as
τ=tzvg=αvgz+12(β222τ03)z21+Bzτ03,
(7)
where α=(β2vg/τ0)[aT+b(aT2aT2)]. Equation 7 can be rearranged as
z=C(Btτ031+αvg)+C2(Btτ031+αvg)2+2Ct,
(8)
where C=2τ03vg/(β22vg+4B). The speed of the non-dispersing wavepacket in its peak position can be written as
vpeak(t)=BCτ03+BCτ03(Btτ031+αvg+τ03BC)(Btτ031+αvg+τ03BC)2+τ03BC(21+αvgτ03BC)=BCτ03[1+sgn(Btτ031+αvg+τ03BC)1+τ03BC(21+αvgτ03BC)(Btτ031+αvg+τ03BC)2],
(9)
where sgn(x) = x/|x|. Hereafter, we assume that α is positive for the sake of simplicity. In this case, the hybrid wavepacket seems to be launched with an initial velocity vpeak(0) = vg/(1+α), which can be modulated by controlling α or aT (see Fig. 5). If B is negative (as is the case in our analyzed waveguide in Fig. 1), vpeak(t) becomes a monotonically decreasing function with respect to t (see Appendix for details). Therefore, the wavepacket always seems to move slower than the initial velocity vg/(1 + α) and its speed slows down with passing time, as was anticipated above. Figure 5 shows a plot of the calculated speed of slow non-dispersing wavepackets plotted in Fig. 3.

Fig. 5 Further slowdown of vpeak of slow non-dispersing wavepackets (i) by modulating the initial launching speeds of hybrid wavepackets (compare the cases of aT = 0 and aT = 1) and (ii) due to their acceleration as they propagate through the waveguide. Solid blue and green dotted lines correspond to hybrid wavepackets associated with the backward and forward modes, respectively.

Through the above discussions, it is possible to identify three different mechanisms involved in the slowness of slow non-dispersing wavepackets: the first is the slow-light feature of the waveguide modes themselves, the second is the modulation of the initial launching speed of hybrid wavepackets, and the third is their acceleration or slowdown as they propagate through the waveguide.

One additional feature of this slow non-dispersing wavepacket that is noteworthy is its spatial trajectory, which can be similarly obtained as
x=(aSβx0)z+12(12β2x03)z2θxzz+12axz2,
(10)
where ax is the acceleration along the +x direction and θxz represents the initial launch angle of the slow non-dispersing wavepacket, meaning the deviation from the propagation coordinate z with the paraxial approximation (θxz = ∂x/∂z). We find that θxz can be determined by the wavevector k⃗ = (aS/x0,β), whose x and z components are given by the initially imposed phase modulation factor and the propagation constant of the waveguide mode, respectively. As was fully discussed in [24

24. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Ballistic dynamics of Airy beams,” Opt. Lett. 33(3), 207–209 (2008). [CrossRef] [PubMed]

], Eq. (10) is equivalent to that describing the constant acceleration motion of particles. When we consider a hybrid wavepacket associated with a backward waveguide mode, β or neff becomes negative for forward power propagation. From Eq. (10) we can see that this negative β does not induce any change in the direction of acceleration, which is determined only by the initial field configuration, which is lacking in spatial symmetry [see Fig. 4(e)]. However, there is one big difference: the initial launch angle θxz retains the sign of β [the wavevector k⃗ becomes (aS/x0, −β)] and its direction flips with respect to z when the waveguide mode becomes a backward one. Therefore, even if the direction of beam acceleration remains the same, the actual trajectory becomes different and thus, the slow non-dispersing wavepackets associated with dual slow-light modes can be separated spatially as they propagate through the waveguide [compare Figs. 3(c) and (f)].

In summary, we showed that slow non-dispersing wavepackets can propagate in plasmonic or metamaterial slab waveguides in a linear optics regime via the association of slow-light waveguide modes with non-spreading Airy wavepackets and nondiffracting Airy beams. Three different mechanisms that contribute to their slow propagation are proposed: (i) the slow-light feature of waveguide modes, (ii) the initial launching speed of hybrid wavepackets which can be easily controlled by changing the configuration of the initial field, and (iii) their acceleration along the time domain in a moving frame. We considered a concrete example, a slab composed of a negative-index ( n=8) core between glass clads, and found that it can support slow non-dispersing wavepackets having an effective propagation speed of ∼ 0.004c0.

Appendix

If ζ(t)=Bt/τ03(1+α)/vg+τ03/(BC), Eq. (9) can be written as
vpeak(t)=BCτ03[1+sgn(ζ(t))1+1ζ2(t)τ03BC(21+αvgτ03BC)].
(11)
We have (t)/dt < 0 when B is negative. If ζ(0) is negative, sgn(ζ(t)) becomes −1 and 2(t)/dt is positive for all t > 0, making vpeak(t) a monotonically decreasing function with respect to t. When ζ(0) is positive, ζ(t) becomes negative when t > t0 where t0=(τ03/B)[(1+α)/vgτ03/(BC)]. If t < t0, we have sgn(ζ(t)) = 1 and 2(t)/dt < 0, and vpeak(t) becomes a monotonically decreasing function. When t > t0, the same conclusion can be drawn since sgn(ζ(t)) = −1 and 2(t)/dt > 0.

If we ignore third-order dispersive effects (i.e., set B = 0 in Eq. (4)), Eqs. (8) and (9) can simply be rearranged as
z=2τ03β22[1+αvg+(1+αvg)2+β22tτ03],
(12)
vpeak(t)=[(1+αvg)2+β22tτ03]1/2,
(13)
where we can find that vpeak(0) = vg/(1 + α), vpeak(t) < vg/(1 + α) for all t > 0, and dvpeak(t)/dt < 0. That is, the wavepacket slows down as it propagates through the waveguide.

Acknowledgments

This work was supported by the National Research Foundation and the Ministry of Education, Science and Technology of Korea through the Creative Research Initiative Program (Active Plasmonics Application Systems).

References and links

1.

J. Durnin, J. J. Miceli Jr., and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987). [CrossRef] [PubMed]

2.

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, and S. Chávez-Cerda, “Alternative formulation for invariant optical fields: Mathieu beams,” Opt. Lett. 25(20), 1493–1495 (2000). [CrossRef]

3.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901 (2007). [CrossRef]

4.

G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32(8), 979–981 (2007). [CrossRef] [PubMed]

5.

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photon. 2(11), 675–678 (2008). [CrossRef]

6.

H. Cheng, W. Zang, W. Zhou, and J. Tian, “Analysis of optical trapping and propulsion of Rayleigh particles using Airy beam,” Opt. Express 18(19), 20384–20394 (2010). [CrossRef] [PubMed]

7.

P. Polynkin, M. Koleskik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324(5924), 229–232 (2009). [CrossRef] [PubMed]

8.

M. Asorey, P. Facchi, V. I. Man’ko, G. Marmo, S. Pascazio, and E. C. G. Sudarshan, “Generalized tomographic maps,” Phys. Rev. A 77(4), 042115 (2008). [CrossRef]

9.

A. Salandrino and D. N. Christodoulides, “Airy plasmon: a nondiffracting surface wave,” Opt. Lett. 35(12), 2082–2084 (2010). [CrossRef] [PubMed]

10.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photon. 4(2), 103–106 (2010). [CrossRef]

11.

C.-Y. Hwang, D. Choi, K.-Y. Kim, and B. Lee, “Dual Airy beam,” Opt. Express 18(22), 23504–23516 (2010). [CrossRef] [PubMed]

12.

M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett. 93(13), 137404 (2004). [CrossRef] [PubMed]

13.

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “‘Trapped rainbow’ storage of light in metamaterials,” Nature 450(7168), 397–401 (2007). [CrossRef] [PubMed]

14.

K.-Y. Kim, “Tunneling-induced temporary light trapping in negative-index-clad slab waveguide,” Jpn. J. Appl. Phys. 47(6), 4843–4845 (2008). [CrossRef]

15.

J. Park, K.-Y. Kim, I.-M. Lee, H. Na, S.-Y. Lee, and B. Lee, “Trapping light in plasmonic waveguides,” Opt. Express 18(2), 598–623 (2010). [CrossRef] [PubMed]

16.

W. T. Lu, Y. J. Huang, B. D. F. Casse, R. K. Banyal, and S. Sridharb, “Storing light in active optical waveguides with single-negative materials,” Appl. Phys. Lett. 96(21), 211112 (2010). [CrossRef]

17.

V. N. Smolyaninova, I. I. Smolyaninov, A. V. Kildishev, and V. M. Shalaev, “Experimental observation of the trapped rainbow,” Appl. Phys. Lett. 96(21), 211121 (2010). [CrossRef]

18.

A. R. Davoyan, I. V. Shadrivov, A. A. Zharov, D. K. Gramotnev, and Y. S. Kivshar, “Nonlinear nanofocusing in tapered plasmonic waveguides,” Phys. Rev. Lett. 105(11), 116804 (2010). [CrossRef] [PubMed]

19.

K.-Y. Kim, I.-M. Lee, and B. Lee, “Grating-induced dual mode couplings in the negative-index slab waveguide,” IEEE Photon. Technol. Lett. 21(20), 1502–1504 (2009). [CrossRef]

20.

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, San Diego, 2001).

21.

I. M. Besieris and A. M. Shaarawi, “Accelerating Airy wave packets in the presence of quadratic and cubic dispersion,” Phys. Rev. E 78(4), 046605 (2008). [CrossRef]

22.

Although we have mainly discussed the slow non-dispersing wavepackets based on metamaterial waveguides, they can also be constructed via the association with other types of slow-light modes such as those in photonic crystal waveguides. Actually, they can be preferred in practice because the propagation loss of slow wavepackets can be significantly reduced. For a comprehensive review, see T. Baba, “Slow light in photonic crystals,” Nat. Photon. 2(8), 465–473 (2008). [CrossRef]

23.

The speed of the center-of-mass position of the hybrid wavepacket remains invariant. Refer to [3] and M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys. 47(3), 264–267 (1979) for more details. [CrossRef]

24.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Ballistic dynamics of Airy beams,” Opt. Lett. 33(3), 207–209 (2008). [CrossRef] [PubMed]

OCIS Codes
(050.1940) Diffraction and gratings : Diffraction
(060.5530) Fiber optics and optical communications : Pulse propagation and temporal solitons
(230.7400) Optical devices : Waveguides, slab

ToC Category:
Physical Optics

History
Original Manuscript: December 21, 2010
Revised Manuscript: January 19, 2011
Manuscript Accepted: January 20, 2011
Published: January 24, 2011

Citation
Kyoung-Youm Kim, Chi-Young Hwang, and Byoungho Lee, "Slow non-dispersing wavepackets," Opt. Express 19, 2286-2293 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-3-2286


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References

  1. J. Durnin, J. J. Miceli, Jr., and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987). [CrossRef] [PubMed]
  2. J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, and S. Chávez-Cerda, “Alternative formulation for invariant optical fields: Mathieu beams,” Opt. Lett. 25(20), 1493–1495 (2000). [CrossRef]
  3. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901 (2007). [CrossRef]
  4. G. A. Siviloglou, and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32(8), 979–981 (2007). [CrossRef] [PubMed]
  5. J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics 2(11), 675–678 (2008). [CrossRef]
  6. H. Cheng, W. Zang, W. Zhou, and J. Tian, “Analysis of optical trapping and propulsion of Rayleigh particles using Airy beam,” Opt. Express 18(19), 20384–20394 (2010). [CrossRef] [PubMed]
  7. P. Polynkin, M. Koleskik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324(5924), 229–232 (2009). [CrossRef] [PubMed]
  8. M. Asorey, P. Facchi, V. I. Man’ko, G. Marmo, S. Pascazio, and E. C. G. Sudarshan, “Generalized tomographic maps,” Phys. Rev. A 77(4), 042115 (2008). [CrossRef]
  9. A. Salandrino, and D. N. Christodoulides, “Airy plasmon: a nondiffracting surface wave,” Opt. Lett. 35(12), 2082–2084 (2010). [CrossRef] [PubMed]
  10. A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4(2), 103–106 (2010). [CrossRef]
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